### Abstract

I re-examine Enderton’s exposition of number theory in his logic textbook, and look at Gödel’s incompleteness theorems, to show that there too definitional extension is both too strong and two weak; the disparity and the resultant ambiguity in both the textbook and the proofs testify to the disparity between the referential discourse of arithmetic and number theory and the analytic discourse of logic. Then I examine parts of Andrew Wiles’ proof of Fermat’s Last Theorem in more detail, since the proof combines disparate discourses in a strikingly ampliative and inspiring way. I also discuss attempts by the logicians McLarty, Friedman, and Macintyre to rewrite the proof and try to show that the aims of logicians are different from the aims of number theorists. This disparity can however contribute to the growth of knowledge as long as both sides tolerate each other and remain open to novel kinds of interaction, with neither claiming to have the Ultimate Discourse.

Original language | English (US) |
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Title of host publication | Studies in Applied Philosophy, Epistemology and Rational Ethics |

Publisher | Springer International Publishing |

Pages | 81-102 |

Number of pages | 22 |

DOIs | |

State | Published - Jan 1 2016 |

### Publication series

Name | Studies in Applied Philosophy, Epistemology and Rational Ethics |
---|---|

Volume | 30 |

ISSN (Print) | 2192-6255 |

ISSN (Electronic) | 2192-6263 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Philosophy

### Cite this

*Studies in Applied Philosophy, Epistemology and Rational Ethics*(pp. 81-102). (Studies in Applied Philosophy, Epistemology and Rational Ethics; Vol. 30). Springer International Publishing. https://doi.org/10.1007/978-3-319-46690-3_5

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*Studies in Applied Philosophy, Epistemology and Rational Ethics.*Studies in Applied Philosophy, Epistemology and Rational Ethics, vol. 30, Springer International Publishing, pp. 81-102. https://doi.org/10.1007/978-3-319-46690-3_5

**Fermat’s last theorem and the logicians.** / Grosholz, Emily Rolfe.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Fermat’s last theorem and the logicians

AU - Grosholz, Emily Rolfe

PY - 2016/1/1

Y1 - 2016/1/1

N2 - I re-examine Enderton’s exposition of number theory in his logic textbook, and look at Gödel’s incompleteness theorems, to show that there too definitional extension is both too strong and two weak; the disparity and the resultant ambiguity in both the textbook and the proofs testify to the disparity between the referential discourse of arithmetic and number theory and the analytic discourse of logic. Then I examine parts of Andrew Wiles’ proof of Fermat’s Last Theorem in more detail, since the proof combines disparate discourses in a strikingly ampliative and inspiring way. I also discuss attempts by the logicians McLarty, Friedman, and Macintyre to rewrite the proof and try to show that the aims of logicians are different from the aims of number theorists. This disparity can however contribute to the growth of knowledge as long as both sides tolerate each other and remain open to novel kinds of interaction, with neither claiming to have the Ultimate Discourse.

AB - I re-examine Enderton’s exposition of number theory in his logic textbook, and look at Gödel’s incompleteness theorems, to show that there too definitional extension is both too strong and two weak; the disparity and the resultant ambiguity in both the textbook and the proofs testify to the disparity between the referential discourse of arithmetic and number theory and the analytic discourse of logic. Then I examine parts of Andrew Wiles’ proof of Fermat’s Last Theorem in more detail, since the proof combines disparate discourses in a strikingly ampliative and inspiring way. I also discuss attempts by the logicians McLarty, Friedman, and Macintyre to rewrite the proof and try to show that the aims of logicians are different from the aims of number theorists. This disparity can however contribute to the growth of knowledge as long as both sides tolerate each other and remain open to novel kinds of interaction, with neither claiming to have the Ultimate Discourse.

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U2 - 10.1007/978-3-319-46690-3_5

DO - 10.1007/978-3-319-46690-3_5

M3 - Chapter

AN - SCOPUS:85019660078

T3 - Studies in Applied Philosophy, Epistemology and Rational Ethics

SP - 81

EP - 102

BT - Studies in Applied Philosophy, Epistemology and Rational Ethics

PB - Springer International Publishing

ER -